\[ \lambda=5 T \quad f=\frac{1}{T} \quad T=\frac{1}{f} \] 12. Cars honk at each other at an intersection. If one car's horn has a frequency of a frequency of 218 Hz and the other horn a frequency of 213 Hz , what will be the PERIOD of the beat that the two horns produce?

To find the period of the beat produced by the two horns, we first need to determine the beat frequency. The beat frequency is the absolute difference between the two frequencies: \[ f_{beat} = |f_1 - f_2| = |218 \, \text{Hz} - 213 \, \text{Hz}| = 5 \, \text{Hz} \] The period of the beat (T) is the reciprocal of the beat frequency: \[ T_{beat} = \frac{1}{f_{beat}} = \frac{1}{5 \, \text{Hz}} = 0.2 \, \text{seconds} \] So, the period of the beat produced by the two horns is \(0.2\) seconds. Now, let’s take a deeper dive into how sound waves and beats work! When two sound waves of slightly different frequencies interfere, they create beats, which are periodic variations in loudness. This cool phenomenon can be experienced in music, where slightly detuned instruments sound harmonious rather than dissonant if they produce beats at a slow rate. Fun fact: The concept of beats isn't just for sound! Musicians often use beats to fine-tune their instruments, and you can even find beat frequencies in light waves too, like when colors mix. So those subtle differences in frequency can lead to some pretty neat auditory experiences!